A previous study has been devoted to the case of optical forces exerted on Rayleigh particles in the framework of generalized Lorenz-Mie theory (GLMT). This study is here extended to the case of small magnetodielectric particles which are characterized by their electric and magnetic Mie coefficients a1 and b1 respectively. A partition of optical forces between incident-scattered mixed terms and recoil terms has been established in GLMT since more than three decades. This partition is here complemented by another partition between gradient, scattering and non-standard forces. The relationship between these non-standard forces and curl forces exhibited in the framework of a dipole theory is emphasized. The case of Rayleigh particles (more generally of electric dipolar particles) previously published in the GLMT-framework is recovered as a special case of the case of small magnetodielectric particles discussed in the present paper. The case of illumination by plane waves furthermore provides complementary insights on the behavior of non-standard forces.